The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras

Abdenacer Makhlouf; Lina Song; Shanshan Liu

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The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras

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arxiv 2111.11015 v1 pith:DOYJZLYP submitted 2021-11-22 math-ph math.MP

Shanshan Liu , Abdenacer Makhlouf , Lina Song This is my paper

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keywords cohomologyhom-pre-liealgebraabeliandeformationsextensionsfullrepresentation

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The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploit strongly the Hom-type structure and fits perfectly with simultaneous deformations of the multiplication and the homomorphism defining a Hom-pre-Lie algebra. Moreover, we show that its second cohomology group classifies abelian extensions of a Hom-pre-Lie algebra by a representation.

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